Topic
Linear approximation
About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.
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TL;DR: A linear approximation by using iteratively Taylor polynomials is presented to solve the Collision Avoidance problem in Air Traffic Management in mixed 0-1 linear terms.
43 citations
TL;DR: These analytical expressions are significant improvements over the existing equations in the literature that are valid only for large κa because the new equations facilitate the modeling of EDL interactions between nanoscale particles and surfaces over a wide range of ionic strength.
Abstract: Exact, closed-form analytical expressions are presented for evaluating the potential energy of electrical double layer (EDL) interactions between a sphere and an infinite flat plate for three different types of interactions: constant potential, constant charge, and an intermediate case as given by the linear superposition approximation (LSA). By taking advantage of the simpler sphere-plate geometry, simplifying assumptions used in the original Derjaguin approximation (DA) for sphere-sphere interaction are avoided, yielding expressions that are more accurate and applicable over the full range of κa. These analytical expressions are significant improvements over the existing equations in the literature that are valid only for large κa because the new equations facilitate the modeling of EDL interactions between nanoscale particles and surfaces over a wide range of ionic strength.
43 citations
TL;DR: This paper proposes a novel level-set method named local approximation of Taylor expansion (LATE), which is a nonlinear approximation method to solve the nonconvex optimization problem of segmentation of images with severe intensity inhomogeneity.
Abstract: Intensity inhomogeneity is common in real-world images and inevitably leads to many difficulties for accurate image segmentation. Numerous level-set methods have been proposed to segment images with intensity inhomogeneity. However, most of these methods are based on linear approximation, such as locally weighted mean, which may cause problems when handling images with severe intensity inhomogeneities. In this paper, we view segmentation of such images as a nonconvex optimization problem, since the intensity variation in such an image follows a nonlinear distribution. Then, we propose a novel level-set method named local approximation of Taylor expansion (LATE), which is a nonlinear approximation method to solve the nonconvex optimization problem. In LATE, we use the statistical information of the local region as a fidelity term and the differentials of intensity inhomogeneity as an adjusting term to model the approximation function. In particular, since the first-order differential is represented by the variation degree of intensity inhomogeneity, LATE can improve the approximation quality and enhance the local intensity contrast of images with severe intensity inhomogeneity. Moreover, LATE solves the optimization of function fitting by relaxing the constraint condition. In addition, LATE can be viewed as a constraint relaxation of classical methods, such as the region-scalable fitting model and the local intensity clustering model. Finally, the level-set energy functional is constructed based on the Taylor expansion approximation. To validate the effectiveness of our method, we conduct thorough experiments on synthetic and real images. Experimental results show that the proposed method clearly outperforms other solutions in comparison.
42 citations
TL;DR: By passing to the limit in the finite element approximations, the existence of a strong solution is demonstrated and semidiscrete error estimates are obtained, and strong a priori estimates for the finiteelement solutions are derived.
Abstract: Semidiscrete finite element approximations of a linear fluid-structure interaction problem are studied. First, results concerning a divergence-free weak formulation of the interaction problem are reviewed. Next, semidiscrete finite element approximations are defined, and the existence of finite element solutions is proved with the help of an auxiliary, discretely divergence-free formulation. A discrete inf-sup condition is verified, and the existence of a finite element pressure is established. Strong a priori estimates for the finite element solutions are also derived. Then, by passing to the limit in the finite element approximations, the existence of a strong solution is demonstrated and semidiscrete error estimates are obtained.
42 citations
TL;DR: In this article, a class of polyhedral norms and a general exchange algorithm for linear approximation problems under these norms were introduced, and a uniform treatment of L 1 and maximum norm problems was given.
Abstract: We introduce a class of polyhedral norms and study discrete linear approximation problems under these norms. It is possible to give a uniform treatment, in particular, ofL 1 and maximum norm problems, at least as regards notation; and we develop a general exchange algorithm in which we permit also linear inequality constraints.
42 citations